Problem A: Deal of Fortune

It is a typical k-SAT model mixed with string manipulation. Yet this problem is not intended as a algorithmically hard problem. A randomized local search will be sufficient.

Problem B: Time Travel

A dynamic programming approach is good for this problem. For further improvement, it can be combined with a shortest path algorithm for graphs with nonnegative arc lengths.

Problem C: Is the Information Reliable?

The task is to determine the satisfiability of a differential constraints system. By using disjoint sets to handle those P tips, rest of the work can be left to the Bellman-Ford algorithm.

Problem D: A New Joseph Problem

Let n be the number of “1” bits in the binary representation of N, then the answer is 2ⁿ − 1.

Problem E: The k-th Largest Group

Use disjoint sets to maintain the groups and use either a segment tree or a binary search tree to find the k-th largest group.

Problem F: A Triangle and a Circle

You have to classify the instances into several classes and handle each of them carefully.

Problem G: Firing

The boss-underling relationship can be modeled by a directed graph. Transformation into a flow network will provide a solution.

Problem H: Function Approximation

Those definitions actually define a continuous piecewise linear function f(x) and and its approximate variant g(x). Perform dynamic programming on the selection of indices i_k to find the optimal approximation.